Quantum Information Copy-Time as a Microscopic Principle for Emergent Hydrodynamics, Inertial Spectral Mass, and a Predictive Higgs-Portal Dark-Matter Corridor

1. Epistemic Status and “Audit-Grade” Rules

We explicitly separate definitions from assumptions and predictions. Table 1 summarizes the labels used throughout.

2. Operational Copy Time and Certification

2.1. Definition of ${\tau }_{\mathrm{copy}}$

Consider a sender region A and a receiver region B, separated by ℓ. Let ${\rho }_0\left(t\right)$ be the evolved state under a reference preparation and ${\rho }_1\left(t\right)$ the evolved state when a calibrated local bias is applied in A at $t=0$. For an allowed class of measurements ${\mathcal{M}}_B$ supported on B, define the certification advantage

$$\mathrm{Adv}(t;\ell )\equiv \underset{M\in {\mathcal{M}}_B}{sup}\left|\mathrm{Tr}M\left({\rho }_{1,B}\left(t\right)-{\rho }_{0,B}\left(t\right)\right)\right|.$$

(1)

Hypothesis 1

(Calibration window). There exists a range of bias strengths such that the disturbance stays below a fixed budget ${\delta }_{\star }$ while the linear-response estimate of $\mathrm{Adv}$ remains valid.

Definition. The operational copy time is

$${\tau }_{\mathrm{copy}}(\ell ;\epsilon ,{\delta }_{\star })\equiv inf\left\{t\ge 0:\mathrm{Adv}(t;\ell )\ge \epsilon \mathrm{under}\mathrm{the}\mathrm{disturbance}\mathrm{budget}{\delta }_{\star }\right\}.$$

(2)

Figure 1 shows the calibrated scaling of ${\tau }_{\mathrm{copy}}$ against information susceptibility in two representative models.

2.2. Certificate Pipeline

The QICT program is designed to be auditable end-to-end: (i) define a measurable target advantage, (ii) calibrate the bias to respect ${\delta }_{\star }$, (iii) certify transfer at distance ℓ by a receiver observable, and (iv) report ${\tau }_{\mathrm{copy}}$ as a reproducible output. The full pipeline is summarized in Figure 2.

3. From Unitary Microdynamics to Diffusion

3.1. Spectral Diffusion Criterion (SDC)

The micro–macro bottleneck is the emergence of diffusion from deterministic unitary dynamics. We replace informal “fast mixing” language by a measurable spectral diagnostic.

Criterion 1 (Spectral Diffusion Criterion (SDC)). Let $T\left(·\right)=U^{†}\left(·\right)U$ be the one-step Heisenberg map of a locality-preserving unitary U (a $\mathrm{QCA}$). We say the dynamics satisfies $\mathrm{SDC}$ if, for sufficiently small wavevector k, the hydrodynamic eigenvalue $\lambda \left(k\right)$ is spectrally isolated and obeys

$$\lambda \left(k\right)=1-D{k}^2+\mathcal{O}\left(k^4\right),D>0.$$

(3)

Theorem 1

(Conditional diffusive lower bound). Assume locality, sector ergodicity, and a quantitative diffusive window validated by the SDC. Then for calibrated protocols satisfying Eq. (2), the operational copy time obeys a one-way lower bound

$${\tau }_{\mathrm{copy}}(\ell ;\epsilon ,{\delta }_{\star })\gtrsim {\displaystyle \frac{{\ell }^2}{4D}}\mathcal{F}(\epsilon ,{\delta }_{\star }),$$

(4)

where $\mathcal{F}$ is an explicit correction originating from inversion of the diffusive tail constraint (Appendix A).

The correction term is operationally important: it induces a strict feasibility boundary for the certificate. Figure 3 illustrates robustness diagnostics for the certificate extraction.

4. Inertial Spectral Mass: A Transport-Mechanical Diagnostic

We define an inertial spectral mass as an operational proxy extracted from the long-wavelength spectral flow of the coarse-grained generator. In a clean diffusive window one expects $\omega \left(k\right)\simeq -iD{k}^2$; in realistic systems one observes crossovers, mode splitting and scale-dependent flows. These deviations can be packaged into a mass-dimension scale extracted from spectral data, which is then compared across sectors and operating points.

Figure 4 shows an example of a flow diagnostic used to quantify stability of the closure window.

5. Analog-Model Validation and Calibration

To assess sensitivity to model choice and calibration details, we include two analog-model validations producing ${\tau }_{\mathrm{copy}}$ and $\mathrm{Adv}\left(t\right)$ curves under the same certificate definition. Figure 5 summarizes this two-model comparison.

6. Predictive Higgs-Portal Dark-Matter Corridor

We consider the real scalar singlet S coupled to the Higgs via ${\lambda }_{HS}{S}^2{H}^{†}H$. The phenomenology is constrained by direct detection, relic abundance, and collider limits. The QICT program contributes a calibration prior by restricting admissible micro–macro closure windows used to propagate uncertainties in the effective parameter extraction.

Figure 6 summarizes a reproducible constraint overlay in the $(m_S,{\lambda }_{HS})$ plane. Figure 7 shows a relic-abundance overlay used as an internal cross-check. Figure 8 shows a grid scan identifying a corridor compatible with the adopted constraint set.

6.1. Likelihood-Style Diagnostic (Illustrative)

To communicate parameter sensitivity without overclaiming a full global likelihood, we include an illustrative “likelihood map” computed from the adopted constraints. This is intended as a diagnostic for where the corridor is most stable to the chosen inputs.

Figure 9. Illustrative likelihood-style map (diagnostic) over the Higgs-portal scan region (grid included).

Figure 9. Illustrative likelihood-style map (diagnostic) over the Higgs-portal scan region (grid included).

7. Reproducibility Package

All figures in this manuscript are generated from the included scripts and data products. The Supplementary file provides additional derivations, robustness checks, and detailed instructions to reproduce each plot.

8. Conclusion

The QICT program elevates “information transfer time” to an operational, auditable observable and shows how it can be used as a micro–macro closure tool. Under explicitly stated and falsifiable assumptions (in particular, a measurable spectral diffusion criterion), the program yields quantitative transport bounds and constrains downstream inference tasks. We illustrated two such targets: an inertial spectral-mass diagnostic for transport and a reproducible Higgs-portal dark-matter corridor. The overall framework is designed so that failures are informative: each assumption is paired with a measurement or diagnostic that can falsify it.